Reverse nearest neighbors Bhattacharyya bound linear discriminant analysis for multimodal classification
Reverse nearest neighbors Bhattacharyya bound linear discriminant analysis for multimodal classification
复制标题
用于多模态分类的反向最近邻 Bhattacharyya 边界线性判别分析
DOI：
10.1016/j.engappai.2020.104033
复制
发表时间：
2021-01-01
影响因子：
8
通讯作者：
Jiang, Cheng-zi
中科院分区：
文献类型：
--
作者：
Guo, Yan-Ru;Bai, Yan-Qin;Jiang, Cheng-zi
近年来，基于Bhattacharyya误差界估计的L2范数线性判别分析（L2BLDA）在适应性和非奇异性方面得到了有效的改进。然而，L2BLDA假设来自同一类的所有样本独立同分布（i.i.d.）。在真实的世界中，这种假设有时会失败。为了解决这个问题，本文将反向最近邻（RNN）技术嵌入到L2BLDA中，提出了一种新的线性鉴别分析方法RNNL2BLDA。RNNL2BLDA不是使用类来构造类内和类间散布，而是使用RNN技术将每个类划分为子类，然后在这些可能包含多个子类的类上定义散布矩阵。这使得RNNL2BLDA摆脱了L2BLDA中的i.i.d.假设，并适用于具有混合高斯分布的多峰数据。此外，通过在RNN中设置阈值，RNNL2BLDA实现了鲁棒性。RNNL2BLDA可以通过一个简单的标准广义特征值问题来解决。在人工数据集、基准数据集以及两个人脸库上的实验结果表明了该方法的有效性。
Recently, an effective improvement of linear discriminant analysis (LDA) called L2-norm linear discriminant analysis via the Bhattacharyya error bound estimation (L2BLDA) was proposed in its adaptability and nonsingularity. However, L2BLDA assumes all samples from the same class are independently identically distributed (i.i.d.). In real world, this assumption sometimes fails. To solve this problem, in this paper, reverse nearest neighbor (RNN) technique is imbedded into L2BLDA and a novel linear discriminant analysis named RNNL2BLDA is proposed. Rather than using classes to construct within-class and between-class scatters, RNNL2BLDA divides each class into subclasses by using RNN technique, and then defines the scatter matrices on these classes that may contain several subclasses. This makes RNNL2BLDA get rid of the i.i.d.assumption in L2BLDA and applicable to multimodal data, which have mixture of Gaussian distributions. In addition, by setting a threshold in RNN, RNNL2BLDA achieves robustness. RNNL2BLDA can be solved through a simple standard generalized eigenvalue problem. Experimental results on an artificial data set, some benchmark data sets as well as two human face databases demonstrate the effectiveness of the proposed method.